[数] 二次规划
In this paper we present a new algorithm for solving quadratic programming problem (QP) with quadratic constraints.
在本文中，我们提出了一种解带有二次约束二次规划问题（QP）的新算法。
The Hybrid Inverse numerical method is a two-step numerical method, comprising of direct matrix inversion and quadratic programming.
混合逆数值算法是一种两步算法，包含直接矩阵反演求逆和二次规划两个步骤。
In the second chapter, we present the basic theory of quadratic programming including conception, optimization al condition and dual problem.
第二章介绍了二次规划的基础知识和基本理论，包括基本概念、最优性条件、对偶问题等；
The key problem of training support vector machines is how to solve quadratic programming problem, but for large training examples, the problem is too difficult.
训练支持向量机的本质问题就是求解二次规划问题，但对大规模的训练样本来说，求解二次规划问题困难很大。
We present a new branchandbound algorithm for solving quadratic programming problem with quadratic constraints, and analyze the convergence of the algorithm.
提出了一种解带有二次约束二次规划问题的新的分枝定界算法对该算法进行了收敛性分析。
According to the standard form of MID system, the problem of mixed integer quadratic programming (MIQP) and its mathematics description can be obtained.
根据混合逻辑动态系统的标准形式，转化为混合整数二次规划（MIQP）的问题，同时获得它的数学描述。
An algorithm of successive quadratic programming(SQP)type is presented to program problems with nonlinear equality and inequality constraints.
建立非线性等式和不等式约束规划问题的一个序列二次规划（SQP）型算法。
Some experiments show that the imposed rotation method derived from quadratic programming is a useful method in elastoplastic analysis of reinforced concrete continuous beams.
试验验证表明，用二次规划求解的强迫转角法是进行钢筋混凝土连续梁弹塑性分析的有效方法。
A mathematic model of road identification problem is provided and the problem is related with a positive definite quadratic programming problem with inequality constraints.
建立了道路识别问题的数学模型并将上述问题与一个不等式约束的正定二次规划问题相联系。
SVM transforms machine learning to solve an optimization problem, and to solve a convex quadratic programming problem by the optimization theory and method constructing algorithms.
它将机器学习问题转化为求解最优化问题，并应用最优化理论构造算法来解决凸二次规划问题。
In this paper a piecewise-linear homotopy algorithm for quadratic programming is developed.
本文发展了一个关于二次规划问题的分段线性同伦算法。
A new iterative algorithm for quadratic programming is obtained when applying the general algorithm to quadratic programming.
把这种算法应用于二次规划，得到了二次规划的一种新的迭代法。
In this paper, penalty parameter for linearly constrained 0-1 quadratic programming is improved.
本文改进了带线性约束0-1二次规划问题的罚参数下界。
Based on the fitting results and its inner law, the calculating efficiency in optimizing the reactor is increased via applying the sequential quadratic programming(SQP) method.
基于其内部规律，结合拟合结果，应用序列二次规划法（SQP）对电抗器进行优化，提高了优化计算效率。
Sequential quadratic programming (SQP) method is an efficient method for solving smooth constrained optimization problems because of its fast convergence rate.
由于序列二次规划（SQP）算法具有快速收敛速度，所以它是求解光滑约束优化问题的有效方法之一。
Finally, axisymmetrical strain analysis program is work out using FORTRAN90 according to parametric finite element quadratic programming method and some key points about the program are explained.
最后，根据参变量有限元二次规划算法，用Fortran90 语言编制轴对称应变分析程序，对程序编制过程中的几个要点进行说明。
Secondly, the optimal flow distribution scheme in which the quadric multiple regression equation is used as the objective function is determined by the quadratic programming.
以这个二次多元回归方程为目标函数，用二次规划方法确定管网的管段流量分配最优方案；
In the first sublevel, the solution of the frictionless unilateral contact problem is obtained by solving an equivalent quadratic programming.
第一层，通过求解与原接触问题等价的二次规划问题来进行结构接触分析；
The theme of this paper is the exploration of algorithm for quadratic programming.
本文的研究主题是二次规划的算法研究。
A region decomposition method to solve a positive definite quadratic programming is presented.
给出了一个求解正定二次规划的区域分解方法。
This method splits the primal problem into two parts, a master problem which is a quadratic programming and several sub-problems which are linear programmings.
该方法的高级问题是一个二次规划问题，而低级子问题是若干个小规模的线性规划问题。
To realize weighting in motion, a method for dynamic locally weighting based on sequential quadratic programming was put forward.
为实现动态称重，提出了基于序列二次规划的动态可局部称重方法。
二次规划（Quadratic Programming, QP）是数学优化中的一个重要分支，属于非线性规划的特例。其核心特征在于目标函数为决策变量的二次函数，而约束条件则是这些变量的线性不等式或等式。其标准数学模型可表示为：
$$ begin{align} min{x} quad & frac{1}{2} x^T Q x + c^T x text{s.t.} quad & A{eq} x = b{eq} & A{ineq} x leq b_{ineq} & lb leq x leq ub end{align} $$ 其中：
核心特征与重要性：
典型应用领域：
求解方法： 凸二次规划（$Q$半正定）有成熟高效的算法：
二次规划是优化领域的关键工具，其特点是二次目标函数和线性约束。当目标函数的二次项矩阵半正定时，问题具有凸性，保证了全局最优解的存在和高效求解的可能性。它在金融、工程控制、机器学习等众多领域有着广泛且重要的应用。来源：INFORMS (Institute for Operations Research and the Management Sciences) 相关出版物及资源。
二次规划（Quadratic Programming，QP）是数学优化中的一个重要分支，主要用于求解目标函数为二次函数、约束条件为线性函数的优化问题。以下是详细解释：
二次规划的标准形式可表示为： $$ begin{aligned} min_{x} quad & frac{1}{2}x^T Q x + c^T x text{s.t.} quad & A x leq b, & C x = d, end{aligned} $$ 其中：
假设需最小化 ( f(x) = x_1 + x_2 )，约束为 ( x_1 + x_2 geq 1 )。
几何解释：在直线 ( x_1 + x_2 = 1 ) 上寻找距离原点最近的点，解为 ( x_1 = x_2 = 0.5 )。
quadprog 函数。CVXOPT、SciPy.optimize 库。二次规划因其在平衡计算复杂度和实际问题建模中的灵活性，成为工程、金融等领域的核心工具。如需进一步了解具体算法或应用案例，可参考运筹学或优化理论教材。
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